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Discrete Kontorovich-Lebedev transforms

RAMANUJAN JOURNAL

Article

Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function K-in(x), x > 0, n is an element of N, i is the imaginary unit, and incomplete Bessel functions. Several expansions of suitable functions and sequences in terms of these series and integrals are established. As an application, a Dirichlet boundary value problem in the upper half-plane for inhomogeneous Helmholtz equation is solved.

Publication

Year of publication: 2020

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ISSN: 1382-4090

Other: 2-s2.0-85090783560

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